Harmonic analyzer and synthesizer apparatus



4 Sheets-Sheet l i. EEEEZQQ M l 4 V inneed 5? I Nov. 24, 1953 w. o. GATES HARMONIC ANALYZER AND SYNTHESIZER APPARATUS Filed Oct. 28, 1950 Nov. 24, 1953 w. o. GATES 2,660,700

HARMONIC ANALYZER AND SYNTHESIZER APPARATUS Filed Oct. 28, 1950 I 4 Sheets-Sheet 2 Inventor Nov. 24, 1953 w. o. GATES HARMONIC ANALYZER AND SYNTHESIZER APPARATUS 4 Shets-Sheet 3 Filed Oct. 28, 1950 lnvenipr Willic'c m QGQ zes Nov. 24, 1953 w. o. GATES 2,660,700

HARMONIC ANALYZER AND SYNTHESIZER APPARATUS Filed Oct. 28. 1950 4 Sheets-Sheet 4 In ven for W z'lliam OGazes 0 his A 9y Patented Nov. 24, 1953 HARMONIC ANALYZER AND SYNTHESIZER APPARATUS William 0. Gates, Beverly, Mass., assignor to United Shoe Machinery Corporation, Flemington, N. J., a corporation of New Jersey Application October 28, 1950, Serial No. 192,662

11 Claims.

This invention relates to improvements in arrangements for analyzing into recordable data movements of machine parts, for example, during a cycle of operation of a machine, and for controlling the movement of machine parts from such data to reproduce a predetermined movement of said parts.

The invention is illustrated as embodied in apparatus for deriving data defining a twodimensional contour in terms of the magnitude of a condition which is a predetermined function of the position of a tool or tracer engaging the periphery of a contour pattern while the pattern is rotated, and for controlling, from corresponding data, the position of a tracing tool to reproduce the said contour upon a rotated workpiece. It is to be understood that in its general aspects the invention is not limited to use in machines of that particular construction.

In the history of automatic control of machine parts, cams and templates have long served as the records of memory devices to remember and control a cycle of relative movement between parts. However, because in its nature a cam or template is inflexible and adapted to rememher only one permutation of movement, the cost of manufacture and storage of the necessary number of records may become excessive. Such nay be the case for example, in machines for working on different styles or shapes of objects, for example, on shoes.

Similarly, these and certain other types of records may sufier from deterioration in storage or use so that the reproduced movement is inaccurate.

Further, a copy of the record, whatever its particular physical form, must generally be present at each location of use. This may multiply the cost of making records and of transporting them, and may involve inconvenience by delays.

Movements of parts in a machine cycle may be subjected to Fourier analysis to provide data, in the form of Fourier coeificients, adapted easily and inexpensively to be recorded, transmitted, or stored, and from which the original movements may be reproduced. Accordingly, an object of the invention is the provision of apparatus by which such data may be employed to reproduce a desired relative movement of parts.

To this end and in accordance with a feature of. the invention, apparatus is provided by which prescribed sinusoidal voltages comprising consecutive harmonic components of a cyclic voltage variation may be generated and summed up to synthesize a voltage wave of predetermined form to control the movement of a machine part to reproduce a required movement.

The illustrated embodiment may be employed either to analyze a, pattern by rotating its edge past a ieeler to develop the pattern, translating the feeler movement into an electric voltage having a wave form corresponding to the developed pattern, and analyzing the resulting wave into its Fourier coefficients, or to trace the outline of a pattern by generating a plurality of sinusoidal voltages defined by their Fourier coefiicients, synthesizing from these voltages a control voltage having the wave form of the developed pattern, and recreating the shape of the pattern by employing the control voltage to guide a stylus in tracing the outline of the pattern. To this end, a pair of rotatable supports are interconnected with the shaits of eight potentiometers, which are geared to rotate in ascending integral ratios of the rotation of the supports, the output of each potentiometer being a voltage proportional to an input voltage times a sinusoidal function of the shaft position.

For analyzing a pattern, a feeler associated with one support is arranged to provide to a selected one of the potentiometers an input voltage which varies with the distance of the feeler tip from the center of the support. The output of the potentiometer is supplied to an integrator whose summation over a cycle of rotation is proportional to an amplitude coefficient for the harmonic corresponding to the shaft rotation ratio. Sine and cosine amplitude Fourier coefiicients are thus easily measured, and from these coefficients, amplitude and phase Fourier coefficients may be conveniently derived as further described hereinafter.

For synthesizing the outline of a pattern, switches are operated to connect each potentiometer to a source of direct voltage proportional to the amplitude coefficient of the corresponding harmonic, the angular position of the potentiometers is adjusted to set in the phase coefficients and the output voltages of the potentiometers are connected in series to provide a control volt age in relation to which a stylus associated with the other support is positioned along a path radially of the support. If the stylus and the rotatable support are both considered as supports or machine parts, then it will be seen that the position of one support or part may be controlled as a predetermined function of the position (i. e. angular position) of the other, the function being predetermined by the Fourier coefficients.

These and other features and objects of the aceoyoo invention will best he understood from con" sideration of the following 'io lzen connection with the accompanying drawings in which,

Fig. 1 is a plan view of an ing the invention, a top panel having been removed to disclose interior 1 go as Fig. 2 is a front elevation a oparatus shown in Fig. 1;

Fig. 3 is a rear elevation of the apparatus closed in Fig. 1;

Fig. i is a partially exploded angular view of a portion of the apparatus disclosed in Fig. l in which the elements are viewed the rear;

and

Fig. 5 is a schematic diagram of the anparatus disclosed in Fig. 1.

Referring to Figs. 2. and 3, the illustrative chine comprises a ii on wl are sup ported a rotatable patt suynort i2 and rotatable workpiece support M. The supports it the frame to. running transversely thereof, is os' plates iii to the frame l= spaced disposition by chine bolts sleeves 22 and nuts E l. Anni 'nateiy halfway fromv top to bottom of the r. nlural tv of shafts 35?, 32, M, at, -z"; front to back of the machine geared together by a train of consecutive integral rota' shafts 32, t l, 35, Eli, That is, when shaft 32 makes two revolutio three revolutions, etc. 1 nected to be driven by a motor ifl ion 52, a gear and pinion on a count and a gear on the shaft is.

The pattern support i2 is con ected 32 through a pair of bevel gears lil spectively secured to the shafts an: workpiece support id is connected. to he s driven by connection to the shaft is tha gear and pinion a countershaft l and a pair of bevel gears fill and respectively secured to shafts l8 and ill. The gearing is such that the supports l2 and M a 1:1 rotation ratio with shaft 3!].

As a pattern P on the support through a cycle of movement by the motor :1 it will be seen that, as viewed along "Efl, radius, the periph :y of the patter" 1 parent movemei inwardly and on center of the support. Further, that a history of the of. the displacement of a peripheryea. at a fixed operating station, c of the instantaneous may a so which is a function the rosit r berifor example, a volt distance of the periphery fro i the of the support along a re. s the instantaneous position or tne refer ence cycle of movement, e. a sec rotation, will provide a record of the contour of ti for the form of the wave of vol spond to the pattern develo To provide means folio:

t c will be periphery of the pattern along a fixed ra 1S,

arm carrying at one end a tracer roll T adapted to the neriphery of the pattern, is supported for radial movement toward and away from the center of support 52 a bracket 92 attached to the frame The bracket 92 has aligned apertures formed by anti-friction rollers it; which allow free movement of the arm 9% only in said directio Teeth St on one side of the arm engage a gear 95.. attached to a shaft I08 extending downwardly through the frame it. A spiral spring I38 3), around the shaft I00 and connected at one end to a collar on the shaft and at the otier end to the frame, yieldingly urges shaft ltd to rotate in a direction to urge the arm it inwardly to keep the tracer T in engagement v. th the pattern during rotation of support 12.

A slider iii- 1; -lg. l) is mounted on. the arm and i" to be moved by the arm over a res-is from a source of direct on 5) to W -LE an outnutvolt lto the ra"al displacement of the tracer the center of the supro t ii.

A -arly wound r ance card iel'il (Fig. 4)

mounted on n insu disk it? at one .Jn of if s iii l respechafts of the series 353, 32, ?.h of the cards is engaged byoa pair mounted on insulating l on of the 5.. its of the series "ts iiw i extend frcntward through i to receive knobs 2G2 (Fi .2) by which card nay he turned to diiierent positions looted by pointers and dials 2515. This nel i l-ii supported on the frame by spacer Til (is-1g. l). The contacts dill are cond to slip rings illl (Fig. 4) which are enl by brushes 25 i resiliently mounted to an insulating bracset attached to one of the plates it. Each resistance card has one terminal connected to a double-throw switch tit (Fig. 5) by which the may be connected either across an adjustable D. voltage source 222 or to terminals of a lllL. throw sv. tch 238 through which output from slider i259 may applied to any seecterl card its or directly to a servo amplifier.

As shown in Figs. 1 and 8, an arm 2513, carrying at one end stylus 252 do. nwardly biased ..y a spring 25 i, is mounted in a bracket 255 similar to bracket 82, to provide for movement of the stylus radially toward and from the 5r the workpiece support it. As best s n in the arm 25%) is arranged to be ven. ir .ardly and outwardly the support :4 by 5%781'119501' to which it is con-- nected by :1 it: engaging teeth on the side of the arm, a siaft 2N and train of eng 3' a on the motor shaft. The motor "l is connected to a servo amplifier (Fig. 5 so that the motor is adapted to position the tilt in predetermined tion to the magnitude of control voltage applied to the amplifier. The follow-up portion of the comprises a resistance ca d 2t?! (F 1) energized from a source of voltage 281. A i ntact 232 is adapted to travel over and to pick from the res nee card voltage which varies with the ption the arm. This followup voltage is connected to the servo amplifier in series with the control voltage it will be .ierstooo'l that the servo amplifier controls the motor Hill to rotate in a direction tending to equalize the control voltage and the follow-up voltage.

The motor 260 is also connected to position the balls 290 of a ball and disk integrator 300 of the type shown on page 25 of Computing Mechanisms and Linkages, Radiation Laboratory Series, vol. 27, McGraw-Hill Book Company, Inc.,1948.

This connection is made through a pair of bevel gears 302 one of which is attached to the shaft 264. Since such integrators are well-known, it will sumce to state that the integrator 300 provides an output comprising the distance of rotation of a cylinder 303 (indicated diagrammatically in Fig. 5) ascertained by noting the degrees of rotation of an indicator disk 304 driven by the cylinder with respect to a fixed pointer 305, which rotation is proportional to If(X1)dXz where the position of the balls is described by the parameter !(X1) and the distance of rotation of an input shaft 305 which drives an input disk 301 of the integrator is described by the parameter X2. This shaft is connected to be driven from shaft I5 through a pair of bevel gears 308 and gears 3I0 and 3I2, the latter being attached to the shaft l5.

As a pattern P on the support I2 is rotated to vary the angle 0 of its cycle position, the output voltage E, of slider I50 will vary cyclically as a function of 0. That is, E;=f(0).

According to the Fourier theorem, the periodic function of 0 can be expanded as follows:

f( 1si o+o+al sin 2a+a +a,. sin (n8I-,,)+ These terms accordingly respectively define the D. C. and the harmonic components of the output voltage Es which harmonic components are voltages each varying sinusoidally at frequencies corresponding to consecutive harmonics of the cycle. Further, the instantaneous sum of a finite number of these components plus the D. C. volt# age component (which may be zero) corresponds to the instantaneous value of the output voltage. The exactness of the correspondence depends, of course, on the extent to which this finite number includes the harmonic content of the function. While the invention is illustrated by apparatus providing eight consecutive harmonics, more or less consecutive harmonics may be employed. At least the first few consecutive harmonics must be provided where, as here, the apparatus is intended to analyze or to reproduce a variety of curves such as those developed from shoe patterns. H

In operation, to analyze the harmonic compo i nents of the output voltage Es with respect to a cycle of rotation of the pattern P on support I2, the switches 220 and 230 are thrown to connect the output voltage of the slider I50 to that resistance card I engaged by contacts 200 which are rotated at a rotation ratio corresponding to the harmonic to be analyzed. For example, in Fig. 5, the switch 230 is shown in position to connect said output voltage to the card engaged by the contacts on shaft 30 for analyzing the fundamental harmonic. The brushes 2I4 engaging the slip rings 2 I 0 on shaft 30 are connected directly, by means not shown, to the servo amplifier, and the knob 202 is set to adjust the card I00 to zero phase angle. In this position when the motor 60 is started and the contacts 200 sweep over the card in synchronism with rotation of the support I2, the voltage taken off the card stated above.

by the contacts will be the voltage applied to the card multiplied by the sine of the angular position 0 of the support I2. The output voltage El of the slider I50 is a function of the angular position of the support I2, that is E';=f(0) as Accordingly the voltage at the brushes 2I4 of the first pair of contacts is f(0) sin 0, while the output of the second pair of brushes 2" will be )(0) sin 20. In analyzing the first harmonic, that is, the fundamental, the voltage f(0) sin 0 is applied to the servo amplifier to control the ball of the integrator. Accordingly, for one rotation of the support I2, the output at the disk of the integrator will be:

A=Kj:'f(0) sin ado 2 By proper choice of K, it can be shown that A will be equal to the amplitude coefiicient A1 of the first harmonic term of the Fourier series:

f(0) +A sin 0+3; cos 0 .4, sin 28+ 8, cos 26+ To obtain E1, the fundamental card, that is the card opposite the contacts rotated -l:l with the rotation of the support I2, is turned by its knob 202 and the integration completed over a second cycle of rotation whereby the disk of the integrator reads:

B=KJ 1(0 cos 0d0=B 4 For recording the fundamental component in terms of its amplitude coefficient in and its phase =tan" and G1=VA1+B1: singe generally,

is determined by connecting the output voltage [Es directly to the servo amplifier to obtain the value of the integral:

21 j; new

This value isltheaveragearoltage of the output series defining the position'oi a support or other machine part as a function of the angular position of a reference cycle. Alternatively, of course, these coefiicients may be derived by mathematical analysis. In addition to other advantages, it will be seen that the definition of a pattern or a cyclic movement in terms of its Fourier coeflicients is particularly adapted for ease in transmission by a telecommunication facility. For example, take the following definition of 7 aishoei sole pattern -as e; function of a 'cycle of revolution: 1 l.

it will be seen that a definition of this pattern couldreadily be telegraphedor telephoned from one "state -.to tanother, .The definition, of course, would comprise eithef-the,magnitude of the sine and cosine coe'fiicients for each harmonic used, or the magnitude and phase coefiicients of each harmonic, and the D. C. coeilicient. The reference cycle; 'e. g."'rotati'cn, would normally be previnusly established, otherwise it must be included in the definition. While acomplete table has been given for] purposes of illustration, it will be {that either set of coetficients' 1A; and Ba er (inland n could be omitted since when oncfset fiff'cceificients'is' given the other is detenfiiriedthereby. When 'n is to tie-calculated from it mayffliefj'reierred to'mark{the dial-"in iour fiua dra'nts' of 90- each as shown in the, drawings, the quadrants being determined in the usual manner. Y

r IiFor Fcontrolling from lsuch "data the ..=mcvement of a tool in relation to a machine cycle, for example, for reproducing the contour' o'f-amattern upon a workpiece W, the workpiece is positioned uponlthe support it. Each resistance card ite is connected by one of the switches 226 to its source of directvoltage-ZZZ, andthe amplitude of this voltage :is adjusted to correspond with the predetermined amplitude coefficient on of the harmonic component related to the rotationratio of its contacts 200, while the card'is positioned by its knob 292 to the predetermined phase angle coeflicient n of the component.

All the sets of brushes-214 are then connected as shown in Fig. 5, .namelyin serieswith .each other and with a source,of'D.C. voltage I hvhich is adjusted to provide a voltage corresponding to the D. C. term andth'e asths'e'veiage applied to theservo amplifier to control thefposition of the stylus252.

When the motor 60 isstartedas the support rotates to vary the angle 8 of itscycle position, the output of the first (or 1:1 revolution ratio) setof contacts will be a1.(sin 0+1), the output of the-second set will beaz (sin 20+:) etc. Accordingly, the voltage supplied to the servo amplifier will correspond to the original function, -)(9), (Eq. 1) and the servom'otorZEG will position the stylus in accordance wit hthe instantaneous value of-the function as related to theinstantaneous angular position of the support it in its cycle so that the outline of the contour of the pattern will betraced on the workpiece;

W. 'If desired,"-o1 course," theFD; C. :term may be introduced in any other or several ways, ior example, .by adjusting the zero position or the stylus. Thus, considering the stylus 252 and the support [A as flrst-andseoond supports or machine parts, there 1 provided apparatus for controlling the position :0! a first support or part' as a function of the position of a second support or part.

Having thus described myfinvention, whatlI claim as new and :desireitmsecure by-L'e'tters Patent of the'United States is:

1. Apparatus for controlling "thepositlon' ota first support having so. rangeot movement i. function OIthe angular poslti'on of a. second sup-' port in a reference cycle of movement comprising, in combination,'meansftor imparting move mentzin a cycle to said second 'supporhmeans for generating a plurality of voltages varying sinusoidally'rwith respect to the sa1d cyclerat con secutive harmonic frequencies of sald'-cycle;-'and means connected tossaid :firsbsupport to 'position it :as aiunction of the magnitude o! B. control voltage comprising the'sum ot'said-voltages. 2. Apparatus as inclaim 1 wherein s'aid gener ating means includes means for adjustlng thc amplitude of each voltage and its phase relation to the-cycle. I I i 3. Apparatus forrcontrolling -the positio'niot: a. first machine 'Jpart having =a'nn'ge or movement as a function-"ct thelpositioncof a second machine part movable in a cycle or movement comprising, in combinaltion, means 1mmovement tosaidsecond part in its cycle oi movement, means for" generating a plurality of conditions having magnitudes measurable in similar units, .said'magnitudesgvaryingcin sinusoidalirclation to said cyclecatxonsecutive'harnionicire quencies thereof, zandameans :tor controlling the instantaneous position. oi: said :flrst; part-gas in function of a magnitudevcomprising'theasumrof the instantaneous-magnitudes bfsiid conditions.

4. In apparatus 'or'the mlass described,:in combination, a first support arranged to -be movable r in a predetermined range-means forlmpartlng to a second support-movementin azpredetermined cycle of movement, electrical means connected with said means for providing a plurality of voltages varying 'sinusoidally with the angular position of' said cycle'at consecutive harmonic frequencies thereof, andzmeansior controlling the position of the first support as a function of a voltage comprising the sum of 'said voltages.

'5. Apparatus as in :claim' 4 and additionally comprising means for varying independently the amplitude 01 each sinusoidal voltage and the phase relation between each ofsaid sinusoidal voltages and the said cycle.

6. In apparatus of the class'described, a first support, a 'rotatable'second support, said first support being movable at an operating station radially of said second-support, a plurality of sine wave voltage generators connected to be second support in consecutive ascending ratios of rotation to provide a plurality of voltages varying in sinusoidal relation to'the angular position of said support in a cycle of rotation and-at consecutive-harmonic frequencies of said cycle, means for varyin'gthe amplitudot the sinusoidal output ofeach generator and the phase relation between said output andthe cycle of rotationo! said support, means 'for connecting said generators to provide a control voltage comprislng'th'e sum of said output-voltages, and servo 'mecha nism for controlling the position of said first support as a function of said control voltage.

7. In apparatus of the class described, a first movable support, a second movable support, servo mechanism for varying the position of the first support responsively to variations in the magnitude of a control voltage, a plurality of rotatable shafts, connections between said shafts and said second support for providing a predetermined relation between the movement of the support and the rotation of one of said shaft and for providing consecutive integral rotation ratios between the remaining shafts and said one shaft, a plurality of fiat linearly wound resistance cards, means for connecting each of said cards to a source of variable D. C. voltage, a pair of contacts connected to each of said shafts for circular movement over said cards to pick off therefrom voltages varying sinusoidally with the rotation of the shafts, means for varying the angular position of each of said cards and means for series connecting the contacts to the servo mechanism to provide a control voltage comprising the sum of the voltages picked off by the contacts.

8. In apparatus of the class described, a movable machine part, a movable support, servo mechanism for varying the position of the support responsively to variations in the magnitude of a control voltage, a plurality of rotatable shafts, connections between said shafts and said part for providing a predetermined relation between the movement of said part and the rotation of one of said shafts and for providing consecutive integral rotation ratios between the remaining shafts and said one shaft, electrical means connected to each of said shafts and arranged each to provide a voltage varying sinusoidally with the rotation of the shaft to which it is connected, means for independently varying the amplitude and the phase of the voltage provided by each of said means, and means for coniii necting all of said means in series to the servo mechanism to provide a control voltage.

9. Apparatus for controlling the position of a machine part as a function of the angular posi tion of a reference cycle comprising, in combination, a machine part arranged to be variably positionable, means for generating a plurality of voltages varying sinusoidally with respect to said cycle at consecutive harmonic frequencies of said cycle, and means for controlling the position of said part as a function of a control voltage comprising the sum of said voltages.

10. Apparatus as in claim 9 wherein said generating means includes means for adjusting the amplitude of each voltage and its phase relation to the cycle.

11. Apparatus for controlling the position of a support as a function of the angular position of a reference cycle comprising, in combination, a movable support, means for generating a plurality of voltages varying sinusoidally with respect to said cycle at consecutive harmonic frequencies of said cycle, and means for controlling the position of said support as a function of a control voltage comprising the sum of said voltages.

WILLIAM -O.GATES.

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